Final answer:
The length segment needed to complete the broadcast is 43 minutes.
Step-by-step explanation:
To find the length of the segment needed to complete the broadcast, we need to subtract the time already allocated from the total airtime. The producer decided to run an 8-minute health segment and a 9-minute science segment, which totals to 17 minutes. The canceled 12-minute celebrity feature is subtracted from this total. So, 17 - 12 = 5 minutes. Finally, we subtract this result from the total airtime of 48 minutes to find the remaining time needed to complete the broadcast: 48 - 5 = 43 minutes.